Need advice for parent's computer purely for Video/Web

My dads old ass e-Machine can't even play a 720p video without chopping up and skipping all over the place. hes been bugging me to price him out a super cheap machine that he can watch 1080p things on his new 27" monitor. Now I was thinking to save on having to get a CPU+GPU, just getting the 3570k since it has the HD 4000 graphics. I have read that it is actually performing well on it stand alone on video of 1080p quality but couldn't find anyone testing it out on that basis alone or having anything to say about it really. Was wondering if I could get some help on this issue, I could plan out the rest just trying to save him some cash if I can just get a CPU alone to do all the video on his comp instead of shelling out for a nice gpu as well. Thanks!!

I believe the AMD APU's (like the A6-3650) would be a better choise for this as they are much cheaper and will easily run 1080p video. Where I live I think I could build a movie machine around one of them for about 250e (brand new excluding windows)

The graphics more than fine. As a company we use quite a bit of onboard graphics machines like this. I actually just built one of these for the folks for Christmas myself. As far as price goes you can probably expect around $500. If you don't want to build it yourself, go to dell and choose an Optiplex 3010 and tweek it to what you want. One thing though, always buy a machine from them with the least amount of memory possible and get it somewhere else. They charge way too much of a premium.

Yeah I plan on building it myself, have built my past few gaming computers and some for a few friends. I just don't want to use my parent's funds and rely on the i5 or as Trathus suggested, the A6 and then get spotty or artifact playback when hes trying to watch some Game of Thrones in 1080p or something =p Want it to knock it out of the park for him. He won't be using it past anything outside watching videos and browsing the web so no need to overkill it with the potential to game or anything else. Just need a solid stand alone CPU that can handle 1080p with no sweat for a resolution that size.

Unless nothing breaks, it should run every video out there for many years. It can be iterated, but I would definitely take a proper GPU instead of relying on the CPU(You can also take an AMD GPU if you wish).
You can switch the i5 to i3 if you wish to drop the price by about $90-100, but Dual-core CPUs are a bit "old" tech in my opinion.

It could also be that your dad's computer is lagging because its bloated with programs and such. A friend's computer had problems with integrated wireless and lagged in Youtube. A reformat fixed wireless and Youtube performance.